Moreover, our performance evaluation procedure based on the \(\langle \mathrm {BEST}_5 \rangle \)  provides just an indication of the ability of a QAMPA solver to identify a good solution of \(\mathtt {WeightedMaxCutGSP}\)  in a reasonable time, and a fully-fledged analysis on comparative advantage of using this method versus other heuristics is required. This analysis has to take into account practical issues such as the effect of noise. The relative performance results will be both problem and hardware dependent. While theoretical frameworks to estimate the impact of noise in circuits featuring XY gates are being developed [1]}, ultimately only the experimental tests on quantum hardware will be able to provide a full picture of performance, including identifying at what layer \(p\)  the solver is most effective. While in the ideal case, performance cannot decrease with \(p\) , under noise the situation is different; performance is observed to decrease quickly with \(p\)  in current hardware [2]}.
QAMPA, with its circuit depth reduction compared to QAOA, will enable empirical studies for higher values of \(p\)  than QAOA on a wide variety of quantum hardware.
Hybridization of QAMPA with adaptive [3]} and recursive [4]} hybrid methods may prove powerful. One advantage of the studied problem, and of others with locally conserved particle number constraints, is that provides a natural error mitigation strategy via post-selection [5]}. Namely, measured bitstrings which do not obey the Hamming weight constraint are discarded. Post-selection has shown to provide significant improvements in experiments on superconducting processors [6]} and can be generally applied beneficially to any situation with constraints.
